But if we play it safe, the problem is that we may be losing out, and I believe we are.

In a way, math isn't the art of answering mathematical questions, it is the art of asking the right questions, the questions that give you insight, the ones that lead you in interesting directions, the ones that connect with lots of other interesting questions -the ones with beautiful answers.

But if we play it safe, the problem is that we may be losing out, and I believe we are.

Bertrand Russell started off as a mathematician and then degenerated into a philosopher and finally into a humanist; he went downhill rapidly!

So in the end it wasn't Gödel, it wasn't Turing, and it wasn't my results that are making mathematics go into an experimental mathematics direction, in a quasi-empirical direction. The reason why mathematicians are changing their working habits is the computer. I think that this is an excellent joke!

I think logicians hate my work, they detest it! And I'm like pornography, I'm sort of an unmentionable subject in the world of logic, because my results are so disgusting!

A random sequence is one that cannot be algorithmically compressed : the shortest description of a random sequence is simply the sequence itself.